SH-60B was (it's now retired) originally a sub hunter, that also did surface surveillance. Later on, it was modified to take Penguin and Hellfire missiles to be able to attack surface targets. Had a Radar, Electronic Surveillance Gear, Magnetic Anomaly Detector, Sonar Buoys and some other toys. For sub work, it carried Mk46 or Mk50 Torpedos.
It has now been replaced by the MH-60R, which is basically the same thing, but they took off the MAD, and added the dipping sonar from the SH-60F (also retired).
Early block MH-60Ss were just Pax, Mail, Cargo logistic helicopters. Made to replace the CH-46 Sea Knight, better known as the Phrog.
Later production MH-60S have Hellfires, Forward Firing 50 Cals and door guns.
Basically, late 90s Navy had/Current Navy Has
SH-2F/G-->MH-60R
SH-60B--> MH-60R
SH-60F--> MH-60R
HH-60H--> MH-60S
CH-46--> MH-60S
H-3 --> MH-60S
They are trying to replace the MH-53 with a 60, but it's too big to realistically replace with the 60. (75,000 pound & 15,000 hp vs 23,000 pound & 3600 hp)
In reality, the MH-53 and C-2A (fixed wing carrier cargo plane) will eventually be replaced by a greater number of Ospreys.